Paper drills normally are used to cut holes in stacks of paper too thick for paper punches. Such drills usually employ bits constructed from a hollow tube with a paper scrap opening at one end and a sharpened hollow circular edge at the other. The sharpened circular edge normally is positioned at the intersection of a conical inner surface and the cylindrical outer surface of the tube. The conical inner surface is formed by cutting on the end of the tube with the apex of a conical sharpening head inserted therein. For such a paper drill bit to work well, its circular edge must be extremely sharp. Once a drill bit has become dull and is full of paper scrap, resharpening becomes a time consuming and difficult operation. Usually the drill bit must be removed from its drill press and placed on a special set up for sharpening by a spinning sharpener. This is time consuming and results in excessive down time of the drilling operation. Therefore, there has been a need to provide an easy to use paper drill bit sharpening apparatus which can tolerate the normal clogged condition of a paper drill bit and does not require the removal of the bit from the drill press or other machinery in which it is mounted.